Thoughts On Economics

Wednesday, January 01, 2020

I study economics as a hobby. My interests lie in Post Keynesianism, (Old) Institutionalism, and related paradigms. These seem to me to be approaches for understanding actually existing economies.

The emphasis on this blog, however, is mainly critical of neoclassical and mainstream economics. I have been alternating numerical counter-examples with less mathematical posts. In any case, I have been documenting demonstrations of errors in mainstream economics. My chief inspiration here is the Cambridge-Italian economist Piero Sraffa.

In general, this blog is abstract, and I think I steer clear of commenting on practical politics of the day.

I've also started posting recipes for my own purposes. When I just follow a recipe in a cookbook, I'll only post a reminder that I like the recipe.

Comments Policy: I'm quite lax on enforcing any comments policy. I prefer those who post as anonymous (that is, without logging in) to sign their posts at least with a pseudonym. This will make conversations easier to conduct.

Saturday, February 17, 2018

Marx can be read as both a continuation and a critique of classical economics.
A not-too-radical reading might emphasize his claim to find distinctions
in economic theory glossed over by classical economists such as
Adam Smith and David Ricardo.
According to Marx, classical economists (as opposed to vulgar
economists such as Frédéric Bastiat,
Jean-Baptiste Say, and
and Nassau William Senior) penetrated beneath
surface phenomena to reveal the anatomy of capitalism.
A more radical reading questions the soundness of the classical
theory, while historicizing its emergence as a
necessary illusion. The spokesmen for
the emerging and progressive capitalist class
sought for a theory justifying their
opposition to aristocrats and the and
the ancien régime. And classical
economics was that theory.

This post presents three distinctions offered in the
first, less radical reading. Marx had great respect
for classical economists. I do not think he
was always fair to them, insofar as he
accused them of error by reading muddle
into them for not seeing his new ideas.
In this post, I do not document this charge
by citing specific passages in, for example,
Theories of Surplus Value.
So more work would need to be done to extend
this from a mere blog post.
(This 8 January 1868
letter
from Marx to Friedrich Engels is apposite here.)
I also put aside the transformation problem here.

First distinction: between labor and labor power.
Marx distinguishes between the capability of a member of
the proletariat to work under the direction or control
of a capitalist and the work done under that direction.
The former is a commodity, labor power. The latter
is the use value of that commodity, that is, labor.
Both Marx and Ricardo treated labor power, like
all commodities, as representing a certain
quantity of embodied labor, namely, the labor
value of the commodities necessarily consumed by the
laborers, taking as given certain conventions
about the hours and severity of work,
the standard of living of the workers,
the size of their families, which members
were expected to work, and so on.

Without this distinction, Ricardo writes about such
nonsense as the labor value of labor. (I need a
direct quote here.) Marx argues that Ricardo is
also unable to explain why capitalists are
able to regularly generate profits. I suppose
one could expand on this to analyze some of
the evident difficulties in understanding
Ricardo.

Second distinction: Between surplus value
and profits, rent, and interest.
Surplus value, for Marx, is the value
added by labor not paid out in wages.
It is an abstraction, akin to
(some of) Ricardo's profits before
his chapter on rent. Marx focuses
on surplus value in the first volume
of Capital.
Surplus value is manifested at a more
concrete level in the form of profits,
rent, and interest on financial instruments.
Would Ricardo's work be better if he
had a separate label for surplus value?

Third distinction: Between
prices of production and labor values.
William Petty, Adam Smith, and David Ricardo
all have a theoretical conception of market
prices and natural prices. Natural prices
are centers of gravity, in some sense, around which
market prices fluctuate. Marx offered a
trichotomy of market prices, prices of
production, and labor values.
The price of production, sometimes called
the cost price, is Marx's equivalent for
Smith and Ricardo's natural value.
Marx can criticize passages in
the classical economists for confusing
prices of production and labor values.
(A further confusion is that between
the labor commanded by and the labor
embodied in a commodity.)

I conclude with noting some complications not to be found in
the above schematic divisions. In speaking of the labor
value of labor power, I am implicitly assuming that all
wages are saved, and that wages are paid in commodities.
But some workers, especially those deemed skilled, are
able to save, even over and above what they need for a
conventional retirement. And wages are paid in money,
with the general level of prices of wage goods only
determined after a bargain with workers has been
struck.

In talking about surplus value, I have ignored
the possibility of profits on alienation.
This case has to be considered in
a complete taxonomy of capital.
Traders
and speculators look for the possibility of
bargains, of buying low and selling high.
Both classical economists and Marx were aware
of this possibility.

In speaking of labor values and prices of
production, I seem to be assuming that all firms
in an industry use the same processes and have the
same costs. But Marx looks at variations in such
processes. (I am never sure whether the processes
that Sraffa takes as given should be the best practice
or an average process. Perhaps, which is correct might
vary among industries.) Finally, one might add a fourth
distinction in Marx's theory of absolute rent, which
is not to be found in the classical economists.

Thursday, February 15, 2018

This post illustrates another fluke case. In this example economy, two techniques
exist for producing a net output of corn. The wage curves for the two techniques
have two switch points. One switch point is on the wage axis, corresponding to
a rate of profits of zero. The other is on the axis for the rate of profits, corresponding
to a wage of zero.

This example is a fluke in two ways. In the jargon I have been inventing,
it is simultaneously a pattern across the wage axis and a pattern over the
axis for the rate of profits. It differs from this previous
example
in that the switch points in both patterns arise for the same pair of techniques.
In my jargon, it is a global pattern.

As usual, managers of firms know of a number of production processes (Table 1).
A single commodity - a ton iron, a ton steel, or a bushel corn in the example - is the output of each process.
Each process lasts a year and exhibits constant returns to scale. Inputs are defined in physical
units, as indicated in the column for the iron-producing process.
All inputs are used up in production; there is no fixed capital or joint production.

Table 1: The Technology for a Three-Industry Model

Input

IronIndustry

SteelIndustry

CornIndustry

Alpha

Beta

Labor

1/3 Person-Yr.

1/2

0.061628

0.420472

Iron

1/6 Ton

1/200

1

0

Steel

1/200 Ton

1/4

0

0.070079

Corn

1/300 Bushel

1/300

0

0

Two techniques are available. The Alpha technique consists of the iron-producing process, the
steel-producing process, and the corn-producing process labeled Alpha. The Beta technique consists
of same iron-producing and steel-producing processes, with the corn-producing process replaced by
the one labeled Beta.

The choice of technique in a capitalist economy is assumed here to be based on cost-minimization
for prices of production.
Prices of production, for each technique, are characterized by a system of three equations
in which the same rate of profits is earned in all three industries, for the processes
comprising the technique. I assume that labor is advanced, and wages are paid out of the
surplus. And I take a bushel corn as the numeraire.

Under these assumptions, one can draw the wage curve for each technique, as in Figure 1.
The outer frontier of the wage curves illustrates the cost-minimizing technique. In the
example, the Beta technique is cost-minimizing whatever the distribution of income.
It is not uniquely cost-minimizing, however, for the switch points. In the two
cases of a zero rate of profits and a wage of zero, any linear combination of the
two techniques is cost-minimizing.

3.0 Conclusion

Suppose the coefficients of production for the corn-producing process in the Alpha technique
were slightly higher. Then no switch points would exist, and the Beta technique would be
uniquely cost-minimizing, whatever the distribution of income between wages and profits.
The coefficients in the example illustrate a boundary case, just as technical progress
creates a situation where prices of production arise for a case of reswitching.
If technical progress were to decrease the coefficients of production for the Alpha process,
the switch points would be closer together and further from the axes. It might
be that what I am now calling a
reswitching pattern
might never occur.
Some other processes for producing iron or steel might supplant the ones in the
example, like in this previous example.

I already have many books on which I am behind, for instance, Anwar Shaikh's Capitalism. I suspect the Penrose biography will strike me like Adelman's biography. I've read some of the economics the subject produced, but did not know about the Nazi-fighting.

Saturday, January 27, 2018

I here provide some notes on a perturbation of an example from Salvadori and Steedman (1988).

Consider an economy in which n commodities are produced in n industries.
In each industry, a single commodity is produced from inputs of labor and the services of previously produced capital goods.
Suppose the technology can be represented in each industry by a continuously-differentiable production function.
The wage-rate of profits frontier for such a model does not contain any switch points.
In other words, for each feasible rate of profits, a single technique is cost minimizing.
Nevertheless, the cost-minimizing technique varies continuously with the rate of profits.
Furthermore, the process associated with the cost-minimizing technique in each industry also varies continuously with the rate of profits.

Suppose, instead, that the processes in each industry were represented by a set of fixed-coefficient processes, instead of
a smooth production function. What would hold in a discrete model that is in the spirit of the neoclassical model?
I suggest that at each switch point on the frontier, 2n wage curves would intersect. In a model
with two produced commodities and two processes available in each industry, four wage curves would intersect at the single switch point.
With three produced commodities, eight wage curves would intersect.
The natural properties for a neoclassical model - if that is what this is - are flukes to several degrees.

I do not necessarily claim anything revelatory from the details of this post. I am testing the applicability of my pattern analysis
by trying it out for various examples.
Although you cannot tell from my presentation, the graphs I draw rely less on numerical approximations than in many of
my earlier examples.
This example is the first I have seen where a pattern with a co-dimension of two or higher
happens to form a one-dimensional locus (curved line) in the two-dimensional slice of the parameter space I graph.
Salvadori and Steedman could have varied their example in an infinite number of ways and still had an example where
all processes varied at a switch point.

2.0 Technology

I make my usual assumptions about technology. At a given point in time, managers of firms know of a number of production processes (Table 1).
A single commodity - a ton iron or a bushel corn in the example - is the output of each process.
Each process lasts a year and exhibits constant returns to scale. Inputs are defined in physical
units.
For example, labor inputs are specified in terms of person-years per ton iron output or per bushel corn output.
All inputs are used up in production; there is no fixed capital or joint production.

Table 1: The Technology for a Two-Industry Model

Input

IronIndustry

CornIndustry

(a)

(b)

(c)

(d)

Labor

1 e1 - σ t

2 e1 - φ t

1

2

Iron

0

0

2/3

1/2

Corn

(2/3) e1 - σ t

(1/2) e1 - φ t

0

0

To produce a self-sustaining net output with this technology, both iron and corn must be produced.
Four techniques can be defined with this technology (Table 2).

Table 2: Techniques in a Two-Commodity Model

Technique

Processes

Alpha

a, c

Beta

b, d

Gamma

a, d

Delta

b, c

I have defined the technology such that coefficients of production decrease with time in
both processes for producing iron. The rate at which they decrease differs between
the two processes.
A more general case would allow for technical process in each of the processes for producing corn.

3.0 A Temporal Path

I first consider the variation with time of prices of production for a special case. Consider:

σ = φ = 1

I make the usual assumptions for prices. Relative spot prices are stationary,
such that the same rate of profits is earned in both industries if the technology
at a given point of time had prevailed over the year. I assume
labor is advanced, and wages are paid out of the surplus at the end of the year.
A bushel corn is taken as the numeraire.
Supernormal profits cannot be made for either process comprising the chosen technique(s).
No process in use incurs extra costs.

Figure 2 shows how cost-minimizing techniques, the maximum rate of profits, and
switch points vary with time. In the region label 1, the Beta technique is
cost-minimizing for all feasible rates of profits.
The Gamma technique is cost-minimizing for high wages and low rates of
profits in Reqion 2. A single switch arises, where wage curves for
the Beta and Gamma techniques intersect on the frontier.
In the language of the technical terminology I have
been introducing, the boundary between Regions 1 and 2
is a pattern across the wage axis. Other patterns are labeled in the
diagram.

Figure 2: Variation of Switch Points with Time

When t = 1, this model reduces to Salvadori and Steedman's example. A single switch exists, with a rate of profits,
r0, of 20 percent
and a wage of (1/5) bushel per person-year. The wage curves for all four techniques intersect at the switch point.
I call the boundary between Regions 5 and 7 a four technique pattern.

I argue that a four technique pattern is of co-dimension two, in my jargon. Each pattern is defined for
a switch point. So, in a pattern, at least two wage curves intersect at a switch point:

wα(r0) = wγ(r0)

The co-dimension is the number of additional conditions that must be satisfied for the
pattern. Here are two more conditions:

wβ(r0) = wδ(r0)

wα(r0) = wβ(r0)

In this example, for any switch point between the Alpha and Beta techniques, all processes are
cost-minimizing. Thus, all techniques are cost-minimizing at such a switch point.
For any set of parameters (σ, φ, t)
at which there exists a switch point on the frontier between
Alpha and Gamma and between Beta and Delta, all techniques are cost-minimizing.
In the example, the first two conditions imply the third because of the processes
of which the techniques are composed. I think this implication does not hold in
general, for all technologies. So I think the definition of a four technique
pattern must include three equalities.

4.0 Partition of the Parameter Space

The above analysis can be generalized, to consider any combination
of (σ t) and (φ t). Figure 1, at the top of
the post, partitions the parameter space into seven regions.
In any given region, the switch points and the wage curves
along the frontier do not vary qualitatively. (Maximum wage,
maximum rate of profits, and rate of profits for switch
points may vary.) Table 3 lists the switch points and wage curves
along the wage frontier, for each region.

Table 3: Cost-Minimizing Techniques

Region

Switch Points

Techniques

1

None

Beta

2

Between Beta & Gamma

Gamma, Beta

3

None

Gamma

4

Alpha & Gamma

Alpha, Gamma

5

Alpha & Gamma, Beta & Gamma

Alpha, Gamma, Beta

6

Beta & Delta

Delta, Beta

7

Alpha & Delta, Beta& Delta

Alpha, Delta, Beta

As an aid to visualization, I present some specific configuration of wage curves. Consider the point in the
parameter space that is simultaneously on the boundary of Regions 1, 2, 5, 6, and 7. At this point,
all techniques are cost-minimizing for a rate of profits of zero. It is simultaneously a four-technique
pattern and patterns across the wage axis. Figure 3 shows the wage curves in this case. For feasible
positive rates of profits, the Beta technique is uniquely cost-minimizing.

Figure 3: Patterns over the Wage Axis

Figure 1 shows loci for four wage patterns intersecting at the point in the parameter space with wage curves illustrated above.
Since six pairs of (unordered) techniques can be chosen from four techniques, one might think that six wage patterns should intersect
at this point. But I am only defining patterns for switch points on the frontier. To illustrate, consider figure 4, which shows
wage curves for a point in Region 5. The wage curves for the Gamma and Delta techniques intersect on the wage axis.
Neither, however, are cost-minimizing here; the Alpha technique is cost-minimizing for a rate of profits of zero.

Figure 4: Wage Frontier in Region 5

Region 7 is the other region in three techniques are cost-minizing along the wage frontier. Figure 5 illustrates Region 7.
For this particular set of parameters, the wage curves for the Gamma and Delta techniques are tangent at a point
within the wage frontier. As far as I can tell, no reswitching patterns arise in this example, for switch points on the
frontier.

Figure 5: Wage Frontier in Region 7

It is also the case that if one extends Figure 1 to the right, the locus for the four-technique pattern never ends.
There is not some set of parameter values where the wage curves for all techniques intersect at the maximum rate
of profits.

In a perturbation of the example, one can find a set of parameters at which the wage curves for all four techniques
intersect at a switch point for a rate of profits of zero. And the parameters can be varied such that the
rate of profits for a switch point for all four techniques can be any positive rate of profits.

Wednesday, January 24, 2018

For we each of us deserve everything, every luxury that was ever piled in the tombs of the dead kings, and we each of us deserve nothing, not a mouthful of bread in hunger. Have we not eaten while another starved? Will you punish us for that? Will you reward us for the virtue of starving while others ate? No man earns punishment, no man earns reward. Free your mind of the idea of deserving, the idea of earning, and you will begin to be able to think. -- Ursula K. Le Guin (21 October 1929 - 22 January 2018)

Saturday, January 20, 2018

I have been considering a case in which a simple Labor Theory of
Value (LTV) is a valid theory of prices of production.
When, for each technique, all processes have
the same organic composition of capital, prices of
production are proportional to labor values.
Given labor values and direct labor coefficients
in each industry, an uncountably infinite number of techniques - as
specified by a Leontief input-output specified in terms
of physical inputs per physical
outputs - satisfies these conditions.

In outlining this mathematics, I start with labor values and
derive technical conditions of production as
a detour on
the way to prices of production.
(I have also considered
a perturbation
of this possibility, as an application of my pattern analysis.)

Has anybody commenting on Marx actually started with labor values, taken as given, in this way?
If this is a straw person, I am good company. Ian Steedman (1977) makes something like the same
accusation. See the section, "A spurious impression", in Chapter 4, "Value, Price, and Profit
Further Considered", of his book.

But I have found examples of other approaching Marx in something like this way.
I refer to von Bortkiewicz (1907) and Seton (1957), two authors taken as a precursor
to the Sraffian reading of Marx. The fact that Steedman can be read as criticizing
such authors complicates the claim that this literature exhibits continuity.
I think others have also argued that some novelty arises in Steedman's
critique insofar as he argues that labor values are redundant, since
prices of production are properly calculated from technical data on
production and the physical composition of wage goods.

Perhaps my examples of Bortkiewicz and Seton should not be
read as propounding any large claim that Marx takes labor values
as more fundamental, in some sense, than physical conditions in
production processes. Rather, Bortkiewicz started from
the schemes of simple and expanded reproduction at the end
of Volume 2 of Capital.
Since Seton, and other authors, were generalizing and
commenting on Bortkiewicz, they, as a matter of
path dependence, happened to keep the assumption of
given labor values.
One wanting to argue for a
reading of Marx that I seem to be stumbling into, without
any firm commitment, needs to deal with Volume 1.

I have two additional notes on rereading these references.
First, I like to talk about Marx' invariants in the transformation problem.
I thought I had taken this term from formal modeling in computer science.
Edsger Dijkstra and C. A. R. Hoare talk about loop invariants, and I sometimes
even comment my code with explicit statements of invariants. But Seton has a section
titled "Postulates of Invariance".

Is Steedman disappointed in the reception of his book? Obviously,
his points about the transformation problem, including the
possibility of negative surplus value being consist with
positive profits, under a case of joint production, have been widely
discussed. But consider his exposition of simple examples
intended to demonstrate that Sraffa's analysis can
take into account all sorts of issues that some had argued
were ignored. Consider letting how much work capitalists
can get out of labor being a variable,
heterogeneous types of abstract labor not reducible to
one and the possibility of workers of each type exploiting
others, wages being paid, say, weekly, during processes
that take a year to complete, how wages relate
to the rate of exploitation when a choice of technique
exists, the treatment depreciation of capital, and
the existence of a retail sector for circulating
produced commodities.
How many of these analyses have been taken up and
continued by those building on Sraffa?
(I think some have.)

References

Eugen von Bohm-Bawerk (1949). Karl Marx and the Close of his System: Bohm-Bawerk's Criticism of Marx. Edited by P. M. Sweezy.

Ladislaus von Bortkiewicz (1907). On the Correction of Marx's Fundamental Theoretical Construction in Third Volume of Capital, Trans. by P. M. Sweezy. In Bohm-Bawer (1949).